Method for generating a model representative of a process

ABSTRACT

A method for generating a model representative of a process. The process includes a result variable representing a product of the process, and a plurality of process variables representing characteristics of the process other than the product of the process. The method includes steps of acquiring a plurality of test values of the result variable; acquiring, for each process variable of the plurality of process variables, a plurality of test values of the process variable, each test value being associated with a result variable value; providing, for each first coefficient of a plurality of first coefficients, a separate test value of the first coefficient associated with each process variable; and, for each second coefficient of a plurality of second coefficients, providing a separate test value of the second coefficient associated with each test value of each process variable.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.11/384,077, which was filed on Mar. 17, 2006 and which issued on Sep. 2,2008 as U.S. Pat. No. 7,421,348. U.S. application Ser. No. 11/384,077claims the benefit of U.S. Provisional Application No. 60/663,461, filedon Mar. 18, 2005.

REFERENCE TO A COMPUTER PROGRAM LISTING APPENDIX

A compact disc and a duplicate copy thereof (a total of two (2) compactdiscs) containing a computer program listing appendix are being filedwith this application. The contents of the compact disc are incorporatedinto this application by reference. Per 37 CFR 1.52(e)(5), the filescontained on the compact disk, along with their dates of creation andfile sizes (in bytes), is listed as follows:

CMCpatentPEMSsql2.txt 17 kb Aug. 7, 2008 CMCpatentReadMe.txt  1 kb Aug.7, 2008

FIELD OF THE INVENTION

The present invention relates to the monitoring and control of processesand to predictive models for their behavior, and more particularly, to aprocess-monitoring and control system and method for predicting aprocess or emissions parameter of an operating emissions source.

BACKGROUND OF THE INVENTION

Public awareness has increased with respect to the environment, andprimary pollutants such as nitrogen oxides and sulfur dioxide arecurrently regulated in most industries, either under 40 CFR Part 60 or40 CFR Part 75. It is the responsibility of the federal EnvironmentalProtection Agency and the individual states to enforce theseregulations. A great deal of attention in recent years has been spent onaddressing the monitoring requirements of these regulations, in order tominimize the discharge of noxious gases into the atmosphere byindustrial facilities.

One technique for ensuring correct monitoring of noxious gases has beento implement continuous emissions monitoring systems (CEMS). Thesesystems are utilized to monitor emissions of sulfur dioxide, nitrogenoxides, carbon monoxide, total reduced sulfur, opacity, volatilehydrocarbons, particulate, and heavy metals such as mercury. Typically,a CEMS is installed in the plant at each emissions source. ApplicableFederal, state, and local regulations include certain options forcontinuous monitoring of each of these emissions sources, and regulatoryagencies are provided with a monitoring plan for each plant that detailshow the emission rate is to be measured and reported prior to startup.

A CEM system typically includes either an in situ analyzer installeddirectly in an exhaust stack, the exhaust pipe of the reciprocatingengine, or in an extractive system which extracts a gas sample from theexhaust stack and conveys it to an analyzer at grade level. Continuousemissions monitoring system components such as gas analyzers are quiteexpensive, difficult to maintain, and difficult to keep properlycalibrated. As such, the regulations that deal with a CEM system requirethe analyzers to be calibrated periodically and subjected to otherquality assurance programming to ensure the accuracy and reliability ofthe compliance data.

In many cases, the regulations allow for certification and operation ofalternatives to the hardware-based continuous emissions monitoringsystem. Such alternatives include software solutions that predict theemissions from available process and ambient parameters. Procedures forcertifying these predictive emissions monitoring systems (PEMS) aredetailed in the regulations, namely 40 CFR Part 75, Subpart E and 40 CFRPart 60, Appendix B, Performance Specification 16. Generally, a PEMsystem models the source of emissions that generates the emissions andpredicts the quantity of emissions that are produced given the operatingstate of the process.

Regulations allow a maximum downtime of ten percent for calibration. Ifa unit remains in operation greater than ten percent of the time withthe CEMS down, the emissions level is considered by the regulators to beat maximum potential level. This results in out-of-compliance operationand over-reporting of emissions. Facilities must maintain and operatetheir gas analyzers to avoid penalties requiring an ongoing operationalexpense and, occasionally, emergency services are required. A reliablesoftware-based PEMS that can be certified under 40 CFR Part 75, SubpartE would represent an extremely cost-effective option of the compliancemonitoring needs of industrial facilities.

There have been PEM systems built in the past to predict variouscombustion and emission parameters from continuous industrial processesand to calculate process or combustion efficiency for compliancereporting and process optimization purposes. Typically, the PEM systemis “trained” by monitoring multiple inputs such as pressures,temperatures, flow rates, etc., and one or more output parameters suchas NO_(x), CO, O₂, etc. After training, in normal operation, the PEMsystem monitors only the multiple inputs and calculates estimated outputparameter values that closely match the actual pollutant levels.Methodologies used in the past include nonlinear statistical, neuralnetwork, eigenvalue, stochastic, and other methods of processing theinput parameters from available field devices and to predict processemission rates and combustion or process efficiency. For the most part,these PEM systems are complicated, relatively costly, and or difficultto implement. These systems also typically require retraining with thesupport of specialized staff from the system provider to adjust theproprietary model to the real-world conditions encountered in the field.

SUMMARY OF THE INVENTION

In accordance with the present invention, a computer system is providedincluding computer readable program code means adapted to perform amethod for generating a model representative of a process, the processincluding a result variable representing a product of the process, and aplurality of process variables representing characteristics of theprocess other than the product of the process.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings illustrating embodiments of the present invention:

FIG. 1 illustrates an overall block diagram of an emissions monitoringsystem in accordance with the present invention;

FIG. 2 illustrates a block diagram of a PEMS computing system inaccordance with one embodiment of the present invention;

FIG. 3A shows a file structure describing values of a process variableand associated coefficients, in accordance with the present invention;

FIG. 3B shows a file structure of a master data table in accordance withthe present invention;

FIG. 4 illustrates a flow diagram for operating the overall system;

FIG. 5 illustrates a diagrammatic view of the statistical hybridmodeling system;

FIG. 6 illustrates a time plot of predicted versus actual pollutantemissions in a test case of a predictive model generated in accordancewith the present invention;

FIG. 7 illustrates a x-y plot of predicted versus actual pollutantemissions in a test case of a predictive model generated in accordancewith the present invention;

FIG. 8 illustrates a time plot of the differences between predictedversus actual pollutant emissions in a test case of a predictive modelgenerated in accordance with the present invention;

FIG. 9 illustrates an overall view of the data flow for compliance.

DETAILED DESCRIPTION

FIG. 1 is a schematic diagram of a system 20 in accordance with thepresent invention for monitoring, predicting, and controlling systemprocess variables and emissions in one or more continuous or batchprocesses and/or emissions sources. The system shown in FIG. 1 isconfigured for centralized monitoring and management of multipleprocesses or emissions sources. Referring to FIG. 1, emissions source(s)101(a)-(c) each run in a continuous or batch process which utilizes rawmaterials (for example, coal or fuel oil) to produce a measurable output(energy or other products). Emission sources 101(a)-(c) can take anyform including reciprocating diesel engines, reciprocating gas engines,gas turbines, steam turbines, package boilers, waste heat boilers,solar-based generators, wind-based generators, fuel-cell basedgenerators, or any other devices that are capable of transforming anyform of potential energy into electricity while exhausting pollutantemissions 102 to the atmosphere through one or more correspondingstack(s) or duct(s) 103 a-c. In FIG. 1, emissions source 101 a andassociated elements of system 20 are shown enclosed in a box A toindicate that these components are located onsite at a power generationfacility or other facility. Elements of system 20 outside of box A maybe sited at nearby or remote locations with respect to emissions source101 a, and may be configured to interface with a PEMS computer 107 (asdescribed below) located onsite proximate emissions source 101 a.Alternatively, PEMS computer 107 may be located remotely from any ofemissions sources 101 a-101 c.

System 20 also uses a novel method for predicting the values of processand emissions variables based on the historical values of the processand emissions variables. The method may be used to generate acomputer-implemented predictive model for predicting the values of thesystem process variables and/or emissions variables. The method forpredicting the values of the process and emissions variables may beimplemented manually. Alternatively, any or all of the steps relating toprediction of the variable values and any or all of the steps relatingto generation of the model may be implemented by or with the aid of oneor more computing devices.

Process and emissions data used to generate the predictive model may beacquired in any of several ways. In the embodiment shown in FIG. 1,process parameter data (for example, temperature or pressure values)relating to a given emissions source 101 a is measured by an associatedprocess control system 105 a. In addition to process control system 105a or as an alternative to the process control system, the process dataor specific portions thereof may be obtained by discrete measuringdevices 199 positioned at various locations along the process stream.Process control system 105 a or discrete measuring devices 199 canmeasure such process parameters as temperature, pressure, differentialpressure, and mass flow. It is understood that the actual processvariables measured by the measuring devices will depend on the processin question.

In the embodiment shown in FIG. 1, emissions data are measured by anassociated continuous emissions monitoring system (CEMS), generallydesignated 198 a, which is coupled to the emissions source. The elementsand capabilities of existing CEM systems are well-known, and will not bediscussed in great detail herein. Typically, CEM system 198 a extractsor receives emissions samples from an associated emission source 101 aand analyzes the samples for constituent components. Based upon theanalysis of such components, information can be obtained about theprocess which generates the emissions. Once this information is known,various process parameters can be adjusted or modified in order tooptimize the process and/or modify the generated emissions.

In addition to process CEM system 198 a or as an alternative to CEMsystem 198 a, the emissions data or specific portions thereof may beobtained using discrete measuring devices 199 a positioned at variouslocations within or around the emissions source. Depending on theprocess in question, CEM system 198 a or discrete measuring devices 199a can measure such emission characteristics as oxides of nitrogen,oxides of carbon, unburned fuel in the emission stream, emission volume,emission heat, emission noise, etc.

It is understood that the actual emission variables measured by themeasuring devices will depend on the process in question. Devices andssystems for measuring gaseous emissions are commercially available fromany of a variety of sources, for example Horiba Instruments, Inc., ofIrvine, Calif. Also, instrumentation and measurement devices to be usedin the collecting data for use in generating the predictive model may besubject to quality controls pursuant to local regulatory requirementsand any site quality assurance programs.

Referring again to FIG. 1, one or more onsite manager stations 111 andone or more onsite operator stations 110 are connected to elements ofsystem 20 to enable a variety of operational and maintenance-relatedfunctions, including real-time monitoring of process and emissionsvariables, monitoring of data quality control activity, systemconfiguration, the generation of process control commands, response tosystem alarms, analysis of process and emissions data, and any of avariety of additional functions. Also, these same functions may beperformed remotely via a laptop computer or other suitable systeminterface device. A remote terminal 150 may access system 20 over aninternet connection 149, and a wireless connection may enable access byanother remote terminal 160.

The steps described herein relating to generation of the predictivemodel of the present invention may be executed manually. However, togreatly increase the speed, efficiency, and flexibility with which thepredictive model is generated, tested, and utilized, and to facilitateuse of the information generated by the model for a variety of purposes,generation of the predictive model and attendant functions such as theacquisition of process and emissions data may be implemented by one ormore computer software elements designed to coordinate and executespecified functions related to generation, testing, and employment ofthe predictive model.

Referring again to FIG. 1, in the computer-assisted implementation ofthe method, historical process and emissions data is gathered andultimately conveyed to a PEMS computing system, generally designated200, where operations are performed on the gathered data and where thepredictive model is generated and implemented. A wired or wireless localarea network (LAN) 109 connects PEMS computing system 200 with processand emissions monitoring systems 198 and 105, with operator workstations110, with supervisor workstations 111, and with any other elements ofsystem 20 as desired. PEMS computing system 200 may be coupled toprocess control system 105, discrete measuring devices 199, and CEMsystem 198 for receiving process and emissions data via one or moreserial ports, via a serial peripheral interface (SPI), a serialcommunications interface (SCI), or via another suitable communicationsinterface.

FIG. 2 shows a more detailed view of one embodiment of the of PEMcomputing system 200. In the embodiment shown in FIGS. 1 and 2, PEMScomputing system 200 includes at least a personal computer or laptopcomputer 107 along with a display or workstation 110 and suitable userinterface devices, for example a keyboard and mouse. PEMS computingsystem 200 is located onsite at the emissions source(s). The PEMSpredictive model is typically generated by and runs locally on a singlecomputing device 107 which provides measured process data, measuredemissions data, predicted emission variable values, and a variety ofother information to workstation 110 and to the various other local andremote workstations previously described.

In the embodiment shown in FIGS. 1 and 2, the software elements orelements comprising the PEM system of the present invention reside oncomputing device 107, generally designated the PEMS computing device. Ingeneral, computing device 107 includes a processor having a speed of 133MHz or greater, at least 512 MB of RAM and, preferably, a fault-toleranthard drive. Examples of suitable computing devices include a personalcomputer (PC), a laptop computer, an engineering workstation, and aserver interfacing with onsite or remotely located client computingdevices. As used herein, the term “PEMS computing device” refers to anycomputing device on which any utility or element of the PEM systemsoftware resides. In the embodiment shown in FIG. 2, PEMS computingdevice 107 contains a data acquisition utility 301, a relationaldatabase application 302, an alarm generation utility 303, a reportgeneration utility 304, a license utility 305, ODBC software and drivers306, and one or more local database files 307.

Referring to FIG. 1, if the process or emissions data requirespre-processing (for example, analog-to-digital conversion) prior tosubmission to computing device 107, suitable processing hardware and/orsoftware may be incorporated into process control system 105, intocomputing device 107, or into the data paths between the various dataacquisition devices and computing device 107. In the embodiment shown inFIG. 1, a multi-channel analog-to-digital (A/D) converter 197 a isincorporated along the data path between controller 105 a and PEMScomputing device 107 for converting analog values of the processparameters to digital values usable by the computing system. Preferably,A/D converter 197 a has a relatively high resolution (20-24 bits orhigher) and is used to improve signal-to-noise ratio of the underlyinganalytical measurements. The signal-to-noise ratio can be measuredonline and automatically optimized by adjusting digital filterparameters either at initial setup, during auto-calibration, orcontinuously online. Alternatively, an A/D port installed in PEMScomputing device 107 may convert analog values received by device 107into digital representations of the measured analog data values.Hardware and software for suitable pre-processing of such data andconversion of data formats is known to those skilled in the art and isreadily available.

It is understood that CEM systems 198 and/or any discrete measuringdevices employed in system 20 may be configured to interface with anyother element of system 20 as required. In addition, any operations orsteps performed by a user may be performed either onsite or remotely viaa remote terminal and a suitable communications interface.Interconnection between the elements of system 20, and onsite and localaccess to elements of system 20, may be provided via any suitablecommunications interface, for example, a wired LAN, a wireless LAN, ordirect wiring between elements of the system. Also, remote access tosystem 20 and to individual elements of the process monitoring andcontrol system may be obtained using any of various means, for exampleinternet connectivity, through a wide area network, or through awireless interface.

It is understood that any or all of the software elements or elementscomprising the PEM system of the present invention may be distributedamong various interconnected onsite or remotely located computingdevices 180, depending on the needs of a particular user or application.It is also understood that a single PEMS computing device 107 may becoupled to multiple emissions sources in order to monitor each sourceand provide predictive emissions and compliance data for each source.

Those skilled in the art will recognize that the distributed dataacquisition, monitoring, and control system illustrated in FIG. 1facilitates acquisition of process and emissions data and communicationof the data to various shared computing resources and user interfacedevices. The system structure shown also facilitates the performance ofsuch functions as the onsite and/or remote monitoring of process andemissions parameters, the calculation of predicted emissions values,issuance of control commands, and the generation of reports or alarms(if required).

To predict the emissions that will be generated by emissions sources 101a-101 c for a given set of process parameters, system 20 uses apredictive model incorporated into a predictive emissions monitoringsystem (PEMS). The predictive model of the present invention isgenerated using actual process and emissions data collected duringnormal operation of the emissions source over a predetermined timeperiod. More specifically, the PEM system uses the historical datacollected during normal operation over a predetermined time period aspart of a training dataset to generate an empirical model for use inpredicting the values of process variables (for example, in an absenceof process data due to a failed sensor or other cause) and emissionsvariables. The accuracy of the resulting predictions is largelydependent upon the range and quality of the training dataset.

FIG. 4 is a process flow diagram showing steps relating to generation ofthe predictive model. Prior to generation of the predictive model,process data is collected at step 425 and emissions data is collected atstep 426 during normal system operation. The process and emissions dataare used in generating a historical training dataset for the predictivemodel. As used herein, the term “process data” refers to any measuredvalues of variables (such as temperature, pressure, volumetric or massflow rate, etc.) relating to a given process. Similarly, the term“emissions data” refers to any measured values of variables (such asconcentrations of specified gases) relating to emissions resulting froman associated process. This first set of process and emissions dataprovides test data values of the process and emissions variables, foruse in generation of the predictive model.

Referring to FIGS. 1 and 4, process variable data (for example,temperature or pressure values) relating to a given emissions source 101is collected by process control system 105 and/or by discrete measuringdevices 199 operatively coupled to the process stream. Process controlsystem 105, discrete measuring devices 199, and CEM system 198 may beactively polled for real-time data, or a manually-generated or automatedrequest may be sent by from an onsite or remote system access node (forexample, operator terminal 110) to provide real-time process parameterdata. Similarly, emissions data is collected by CEM system 198 and/or bydiscrete measuring devices 199 positioned at various locations within oraround the emissions source(s).

The process and emissions data is collected over a predetermined timeperiod and is characterized according to such features as data type (forexample, temperature, pressure), data source (i.e., the particular fieldoperating device from which the data was received), and minimum andmaximum values of the data from a given source. The collected processdata and emissions data are then pre-processed in step 426 a, ifrequired. For example, it may be necessary to convert analog dataprovided by the measuring instruments to digital data manipulable bydigital computing devices, if the data quality assurance methods and/orother operations to be performed on the data are computer-assisted.

Data values are measured at a base sampling interval (BSI) which isdetermined according to a known response time of an emissions variableto a change in a process variable. A finite amount of time is requiredfor a change in the process to affect the emissions. For processes whichproduce gaseous emissions, the length of this time period generallydepends on such factors as the exhaust gas path and the samplinglocation. For most industrial processes, at least a minute is requiredfor a change in a process variable to change the emissions as measured.For most boilers, for example, the BSI is set to approximately oneminute. For gas turbines, the BSI can range anywhere from approximately1 minute (in large units) to 10 seconds or less (for smaller units). Forsome high-speed industrial processes such as arc welding, the BSI may beset below 1 second. Each measured data value is addressed and labeledfor reference purposes. In a computer-assisted implementation of themethod, the labeled data is then incorporated into one or more recordsin a relational database.

Referring to FIGS. 1 and 2, in a computer-assisted implementation of themethod, process and emissions data from CEM system 198 a and/or discretemeasuring instruments 199 a is received by a data acquisition element301 residing in PEMS computing device 107. Data acquisition element 301is configured to query and to enable querying of CEM system 198 a and/ordiscrete measuring devices 199 a for associated process and emissionsdata. Data acquisition element 301 may be configured by a user to avariety of operational modes. For example, element 301 may be programmedto query CEM system 198 a or measuring devices 199 a upon startup oractivation of the PEM system, upon receipt of a command from a user atPEM computing device 107, or automatically on a regular basis atpredetermined intervals. In other modes of operation, element 301 mayreceive process and/or emissions data forwarded automatically atpredetermined intervals by CEM system 198 a or devices 199 a or inresponse to a query initiated from a user at a remote computing device.Other operating modes and events resulting in transmission and receiptof process and emissions data are also contemplated.

In step 426 a, the measured process and emissions data is alsostructured into one or more records in a relational database whichdefine a raw data database. Compilation and organization of the data maybe accomplished by a portion of the PEMS application, or the compilationand organization may be accomplished using another, commerciallyavailable application, such as Microsoft® ACCESS, dBase™, DB2, astandard spreadsheet program such as Microsoft® Excel, or anothersuitable database platform. However, any database platform used tostructure the gathered data is preferably accessible using Open DatabaseConnectivity (ODBC) programming statements, or using programmingstatements conforming to a comparable standard that permits querying ofthe database using Structured Query Language (SQL) requests.

In the computer-implemented embodiments discussed herein, interactionbetween the relational database(s) of the present invention andinteraction between a user and the databases is conducted usingStructured Query Language (SQL) requests. These requests may, forexample, may be formulated as required, previously structured into SQLprogramming segments, or may be previously embedded in applicationsprograms or other programs.

As known in the art, the SQL requests are processed by the databasemanagement system (DBMS), which retrieves requested data elements fromthe relational database and forwards the data to the requesting entity,for example a human operator located at an onsite or remote systemaccess point. Storage of the process and emissions data and informationassociated with the data in relational database(s) and the use of SQLstatements to interact with the database(s) provides operators or othersystem users with enormous speed and flexibility with regard toaccessing and manipulating the stored data. For example, a user candefine the organization of the data, determine relationships between thedata elements, conduct searches for data elements meeting user-definedcriteria, and dynamically modify the database by rearranging elements,adding elements, removing elements, and changing the values of existingdata elements.

Interaction between the relational database(s) of the present inventionmay also be conducted using Dynamic SQL statements, which facilitate theautomatic generation of queries. Such statements can be entered by auser or programmer, or they may be generated by a program.

In the embodiments described herein, PEMS computing device 107interfaces with process control system 105 a, discrete measuring devices199 a, and other elements of system 20 via a set of standard datainterfaces known as Object Database Connectivity (ODBC). As is known inthe art, ODBC translates an SQL request into a request the databasesystem understands, thereby enabling the database to be accessed withoutknowing the proprietary interface of a given database application. TheODBC or other interface software and associated drivers for accessingthe process and emissions data files application are incorporated intothe computing device on which the database is stored and on any remotecomputing devices through which database access may be requested.

Separate data streams from different process or emissions monitoringdevices may be entered into different database applications, dependingon such factors as the equipment being used and the geographic locationsof the emissions sources. Preferably a single type of database platformis used to store process and emissions data for each emissions source.Alternatively, the raw data may be retained in memory in one of variousalternative file formats for further manipulation prior to incorporationinto a database. Formatting of the data is generally undertaken (inconjunction with the chosen database application) by the dataacquisition element of the software, but may alternatively beaccomplished by another portion of the PEMS program if so desired.

Returning to FIG. 4, in step 427, the emissions data and process dataare time-correlated such that there is a record for all values of eachvariable for each base sampling interval. This provides a commontemporal reference frame for all measured data values.

In step 427 a, the raw data from CEM system 198 and/or measuring devices199 is quality assured per 40 CFR Part 60, Appendix A, incorporatedherein by reference. The data may be quality assured either manually orusing automated methods. Data values measured during a period ofcalibration are replaced with process data from surrounding records (ifappropriate) or flagged for removal from the data set. Data that will beretained for further analysis is adjusted for bias and drift.

In step 428, the raw data is adjusted to match the timing of the basesampling interval.

In step 429, all calibration data (data obtained and used forcalibrating field devices 104), maintenance data (data obtained duringemissions source maintenance period or procedures), and non-operatingdata (such as data obtained when the emissions source is offline) areeliminated.

In steps 430 and 431, the data is analyzed in accordance with proceduresoutlined in 40 CFR parts 60 and 75, incorporated herein by reference.Calibration adjustments are made and erroneous or invalid data isotherwise eliminated.

As stated previously, the steps for generating the predictive model ofthe present invention may be executed manually. However, to greatlyincrease the speed, efficiency, and flexibility with which thepredictive model is generated, tested, and utilized, and to facilitateuse of the information generated by the model for a variety of purposes,generation of the predictive model as well as attendant functions suchas the acquisition of process and emissions data may be implemented byone or more computer software elements designed to coordinate andexecute specified functions related to generation, testing, andemployment of the predictive model.

For simplification, the following describes the generation and operationof the predictive model for a single process or emissions source. Itwill be understood that the methodology described herein can be repeatedfor each process or emissions source to be monitored and controlled. Thestatistical hybrid method utilizes standard statistical operations onthe historical training dataset (average, correlation, standarddeviation, confidence, and variance) along with a fixed set of tuningcoefficients that are more typically found in non-linear statistical andother advanced empirical predictive models. The resulting hybrid methoduses built-in statistical SQL data processing structures and the hybridtuning coefficients to transform the current process vector against thehistorical training dataset and to find predicted values. A method forderiving optimum values of the hybrid tuning coefficients from thehistorical training dataset is provided herein and may be used toautomatically build a statistical hybrid model in the embodimentdescribed herein.

Referring again to FIG. 4, at step 432, a change vector or delta valueis calculated from each pair of time-successive measured test values ofeach process variable. As used herein, the term “time-successive” asapplied to the measured data values is understood to mean a firstmeasured value and the another measured value measured at a pointclosest in time to the first value, either before or after measurementof the first value. For each current value of the process variable, thechange vector is generated by subtracting the last value of the processvariable from the current value of the process variable. For example,the change vector v_(c) for two successive measurements of a temperatureparameter T would be equal to T_(t)−T_((t-Δt)) (i.e., the temperature attime t at which a first temperature measurement was taken, minus thetemperature at time t-Δt when the previous temperature measurement wastaken.) The change vector represents the change in a given processvariable over the sampling interval. Once calculated, the calculatedvalues of the change vector may be added to an additional data field inthe data file for the process variable. Alternatively, the change vectorvalues may be stored in another record in the relational database.

In step 433, using suitably formulated SQL statements, a value for theTSLU is then calculated for each corresponding measured value of theprocess variable. The TSLU is an arbitrary number representing in itssimplest form, the Time Since Last Upset an operating state of theprocess. This simplest embodiment is an integer representing the timesince the last process upset was recorded in minutes. A given model canuse multiple TSLU values to delineate distinct operating modes. Anotherexample would be if a unit has six distinct operating modes, then TSLUcould be 1 through 6. Alternatively the TSLU can be defined as 1000through 1999 for mode 1, 2000 through 2999 for mode 2, etc. with thefirst digits (thousands) representing the operating mode and the nextthree digits representing the time since last upset in the operatingmode as defined previously. The TSLU allows the model to predictemissions with temporal and mode specific variability, an advancementover previous statistical (linear and non-linear) models.

If the TSLU is measured in units of sampling interval, for example, witha sampling interval of one minute, a TSLU of 3 would indicate a processchange in the past equal to three times the sampling interval at whichthe process variable was sampled to provide test data or three minutesago. In cases where all of the measured values of the process variableare less than the corresponding initial tolerance for the measuredvalue, the TSLU's are set to 0. In this condition, the unit is offline.For each value of the process variable, the time since last upset isreset to 1 if the change in the process variable (from the previousmeasured value of the process variable to the current measured value) isgreater than the initial tolerance. If there is no change in themeasured value greater than or equal to the initial tolerance the timesince last upset is incremented by adding 1 sampling interval to theprevious value of the TSLU. In this respect, the TSLU is an indicatorvariable which provides a running total of the number of samplingintervals that have elapsed since the occurrence of a change in theprocess variable that exceeded the initial tolerance for that processvariable. Successive values of the TSLU are added to a field in the datafile for the process variable. Incorporation and pre-processing of thehistorical training dataset is now complete.

Referring to FIGS. 3 b and 4, in step 434, the current version of thedataset, including the process and emissions data, the changes for eachprocess vector, and the time since last upset is imported into therelational database as a master data table. FIG. 3 b shows one exampleof a data structure embodied in the master data table. The datastructure includes one or more data elements identifying an associatedprocess or emissions data value, the data value itself, and associatedvalues of the various coefficients (TSLU, delta, etc.) previouslydescribed. Other information relating to the process or emissionsvariable, or to a particular value of the variable, may be incorporatedinto the file structure as required.

In step 435, this version of the historical training dataset is then putinto production and assigned a serial number which represents the numberof records in the training dataset table and the date and time of thecompletion of importation of the dataset for use in compliancemonitoring.

In step 436, correlation factor is calculated to provide a quantitativeindication of a correlation between the emissions variable to becalculated and the associated process variable. In one embodiment, thecorrelation factor is a linear correlation coefficient As is known inthe art, the correlation coefficient is a value between −1 and 1 whichindicates the closeness of the relationship between two variables to alinear relationship. The closer to 0 the correlation coefficient is, theless likely there is to be a linear relationship between the twovariables. Conversely, where the correlation coefficient is close to 1,there is a strong linear relationship between the two variables. Themethod of the present invention focuses on the relative strength of thecorrelation between two variables, rather than on whether thecorrelation between the variables is positive or negative. Thus, theabsolute value of the correlation coefficient is used in the presentmethod for evaluating the strength of the correlation. Methods forcalculating the correlation coefficient using a set of values for eachvariable are well-known.

In addition, each variable is provided with an initial tolerance valuethat is stored in the configuration file with the model setup. Atolerance value is derived for each input variable from the historicaldata contained in training dataset by using a standard statisticalfunction (for example, standard deviation) and scaling the variable inquestion relative to the remainder of the input variables. The tolerancefor each input variable represents a signal-to-noise ratio for the givenhistorical training dataset and is calculated such that a change in theinput variable value equal or greater to the tolerance is significant(not just an incidental variation caused by random fluctuations in themeasurement). In step 437, the standard deviation for each processvariable is calculated and a tolerance for each process variable is setto a value of one-tenth of the standard deviation. This value (0.10) iscalled the initial global configuration parameter and can be adjustedmanually or automatically by the system to maximize accuracy andresiliency to input failure. Alternatively, in cases where processvariable data is available for a period of normal operations includingstartup and shutdown of the process, the standard deviation is computedfor the measured values of the process variable over the measurementcycle, and an initial tolerance for the process variable is set toapproximately one half the standard deviation. In cases where processvariable data is unavailable for such a period of normal operations, theinitial tolerance for the process variable is set to approximately 2.5%of the range (maximum-minimum) of the measured values of the processvariable. Numerous methods for calculating the initial tolerances arecontemplated, and an optimum tolerance setting may be calculatedautomatically based on the historical training dataset.

Increasing the number of data points for a variable in the trainingdataset (for example, by decreasing the sampling interval or by takingmore data samples over a longer time total period) allows the value ofthe corresponding global configuration parameter to be decreased,resulting in increased accuracy of the model. However, there is atradeoff when structuring the SQL statements for the predictive model inthat the greater the number of data points for a parameter in thetraining dataset and the lower the value of the corresponding globalconfiguration parameter, the more system resources are required toprocess the data at a given base sampling interval.

In step 438, following collection of the data comprising the historicaltraining dataset, standard statistical tools are used to analyze therelationships between the process variables and the emissionsvariable(s) to be predicted. The variables and variable changes arecategorized into groups based on the statistical correlation of theprocess variables to the emissions variable sought to be predicted. Theprocess variables are classified in one of the following categories:

Load variables (LV)—A load variable is a variable that is independent ofthe process state and which fundamentally changes the operating profileof the emissions source when the variable experiences a change of valueequal to or greater than a tolerance assigned to the variable. Loadvariables are set by the operator according to the load demand on theemissions source. Load variables typically fall within the top 10% ofprocess variables having a correlation coefficient greater than 0.50with respect to the emission variable to be predicted. Load variablesare always used in generation of the predictive model, but are notneeded for regulatory compliance reporting.

Critical Load variables (CLV)—A critical load variable is a variablethat is either critical to predicting the value of the desired variable,or critical to the compliance reporting requirements for the emissionssource. Critical Load variables are always used in generation of themodel or are always needed for regulatory compliance reports. CriticalLoad variables also typically fall within the top 10% of processvariables having a correlation coefficient greater than 0.50 withrespect to the emission variable to be predicted.

Criteria variables (CV)—Criteria variables have significant correlation(relative to the other input variables) to the predicted value ofdesired variable. Criteria variables typically fall between the top 10%and the top 33% of process variables having a correlation coefficientgreater than 0.50 with respect to the emission or other variable to bepredicted. Criteria variables are used frequently in generation of themodel, but are not critical for predicting the value of the emissionsvariable.

Non-Criteria variables (NCV)—Non-Criteria process variables are thosevariables which show no discernable correlation to the variable to bepredicted. Non-criteria variables typically fall between the top 30% andthe top 50% of process variables having a correlation coefficientgreater than 0.50 with respect to the emission variable to be predicted.Non-criteria variables are sometimes used in generation of thepredictive model, but are not critical for predicting the value of theemissions variable.

Process variables having correlation coefficients below 0.50 withrespect to the emission variable to be predicted are not used ingeneration of the predictive model. Any calculated variables (forexample, combustion efficiency) are categorized as restricted variables.These variables are restricted from storage in the historical databaseand are stored in a compliance database.

In step 440, using the data gathered for the historical trainingdataset, the structured query language (in source code) for thepredictive model is developed. This can be done either manually orautomatically by the system using the procedures and software describedabove.

In step 441, the predictive model for the emissions source is now fixedand ready for testing.

In step 442, a Subpart E analysis is performed on the predictive modelas described in 40 CFR Part 75, Subpart E, incorporated herein byreference.

In step 443, it is determined whether the Subpart E analysis results areacceptable. In step 444, if the Subpart E analysis results areacceptable, the predictive model is put into real-time mode. In step445, the model is certified per Federal regulations prior to utilizationfor compliance reporting purposes.

Referring now to FIG. 5, there is illustrated a block diagram showingoperation of the predictive model as it generates predictions ofemissions or process variable values. The procedure will be describedfor generating a prediction of a desired emissions variable based on themeasured values of selected process variables. However, it will beunderstood that this procedure may be applied to predict a value of aprocess variable given simultaneously-occurring values of other processvariables and one or more associated emissions variables.

At step 546, new process data is collected at the base samplinginterval. This set of data provides comparison values of the variables,for comparison with the test values of the variables stored in themaster data table. As the process data is acquired, it is evaluated forvalidity and input variables are flagged with statuses reflecting theperceived state of the input (as valid or invalid). Invalid data is notused for comparison with the model, however, other data and/or data fromother process variables can typically provide enough information togenerate a valid prediction if one or more of the data acquisitiondevices has failed and is providing invalid data.

In steps 547 and 548 values of the variables determined during modelgeneration to be load and critical load variables (and contained in theproduction copy of the master data table) are evaluated to determine ifthe model is valid for current values of the process data. The values ofthese variables in the new dataset should be within the tolerancescalculated and associated with these load and critical variables ascompared to each record in the historical training dataset. At least aminimum number of new dataset variable values and associated coefficientvalues are required to be matched to corresponding records in the masterdata table depending on the regulatory regime the compliance monitoringsystem is to be deployed under.

In step 549, the TSLU's for the newly acquired process variable valuesare calculated, as previously described.

In step 550, the change vectors for the new set of process variablevalues are calculated, as previously described.

In a typical example or how the predictive model may be used, it isdesired to generate a predicted value of a desired emissions variableunder certain specified process conditions. The method of the presentinvention identifies key process variables that have the greatest impacton the value of the desired emissions variable and uses the values ofthese key variables under the specified process conditions as searchcriteria to query the master data table for a match.

It is desirable to generate the predictive model based on a sequentialelimination of the least critical variables (i.e., eliminating from thesearch criteria, in descending order, the process variables having thelowest correlation coefficient) until a valid match is found. Thus,consideration of each input variable would be reduced to the mostsignificant load and critical compliance variables in succession, one ata time. In one embodiment of the present invention, the processvariables are grouped by significance into load, critical compliance,criteria, and non-criteria variables, as described above, which allowsthe predictive model to iterate through SQL statements, limiting thecalls to the database to a maximum of 10 attempts. In otherapplications, a greater or lesser number of query attempts may be used.Using this system, common, commercially available computers (forexample, personal computers) possess processor speed and databasecapabilities sufficient to generate valid predictions every 10 secondsat a base sampling interval of 1 minute. The most desirable solutiondescribed above would iterate through each variable potentiallygenerating hundreds of database calls with each attempt.

In step 551, the master data table is surveyed for data valuescontaining a match (within the associated tolerances) for each of theload variables and their associated deltas and TSLU's, each of thecritical load variables and their associated deltas and TSLU's, each ofthe criteria variables and their associated deltas and TSLU's, each ofthe non-criteria variables and their associated deltas and TSLU's. Themaster table may be surveyed in this step and in the following stepsusing a structured query statement to the master data table whichelicits the desired information.

In step 552, if the survey yields a positive result (i.e., a match isfound), the value of the desired emissions variable corresponding to thematched value of the process variable is taken as the predicted value ofthe emissions variable for the current process. This value may beforwarded to a user or incorporated into a compliance database forgeneration of reports of other uses (step 571).

In step 553, if the first query yields a negative result (i.e., nomatches are found), the query is repeated with the load variables andtheir associated deltas and TSLU's, and the criteria variables and theirassociated deltas and TSLU's at initial tolerance.

In step 554, if one or more matches are found, the value of the desiredemissions variable in the master table corresponding to the matchedprocess variable values is taken as the predicted value of the emissionsvariable, as described above.

In step 555, if the second query yields a negative result, a third queryis generated using the load variables and their associated deltas andTSLU's, and the criteria variables and their associated deltas andTSLU's at double the initial tolerance of the variables.

In step 556, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 557, if the third query yields a negative result, a fourth queryis generated using the load variables and their associated deltas andTSLU's, and the criteria variables and their associated deltas andTSLU's at triple initial tolerance.

In step 558, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 559, if the fourth query yields a negative result, a fifth queryis generated using the load variables and their associated TSLU's, andthe criteria variables and their associated TSLU's at initial tolerance.

In step 560, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 561, if the fifth query yields a negative result, a sixth queryis generated using the load variables and their associated TSLU's, andthe criteria variables and their associated TSLU's at double initialtolerance.

In step 562, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 563, if the sixth query yields a negative result, a seventhquery is generated using the load variables and their associated TSLU's,and the criteria variables and their associated TSLU's at triple initialtolerance.

In step 564, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 565, if the seventh query yields a negative result, an eighthquery is generated using the load variables and their associated TSLU'sat initial tolerance.

In step 566, if a match is found, the predicted value of desiredemissions variable is assigned as explained above.

In step 567, if the eighth query yields a negative result, a ninth queryis generated using the load variables and their associated TSLU's atdouble the initial tolerance.

In step 568, if a match is found, the desired emissions variable areprocessed as explained above.

In step 569, if the ninth query yields a negative result, a tenth queryis generated using the load variables and their associated TSLU's attriple the initial tolerance.

In step 570, if no match is found, the predictive model defaults to analternative predictive scheme (step 572). For example, an AppendixE-type model approved by the Federal regulations as an alternative canbe used at this point. Alternatively, the predictive model of thepresent invention may iterate through each process variable from leastto most significant if the hardware and software platforms in use havesufficient capability.

When a valid prediction is achieved, it is output to the control system,the data acquisition system, or published locally where it can bereviewed for processing of alarms. The predictions are also stored in acompliance database that is not editable and maintains a continuoussecure location for compliance emission data.

In step 574, the previous values of the variables are updated for thenext calculation of the change vector prior to repeating at the basesampling interval. Each new process vector (each acquisition of thereal-time data from the process) is processed independently. This allowsthe system to process either batch or continuous process data. Theacquired data is sequential, in that one data value for each variable isgathered at each base sampling interval, enabling the deltas to becalculated properly. The reset is done each time the current processvector is processed. The previous values of the variables are retainedonly to calculate the deltas for the next record.

In one example, on a typical gas turbine application under 40 CFR Part60, the base sampling interval is set to 1 minute and the requiredmatches in the historical training dataset is 1 record. Each minute, theprocess vector is acquired and then processed into a SQL statement forcomparison with the historical training dataset. The resulting outputvector includes the empirical emissions data contained in the trainingdataset valid for the current process condition reflected in the processvector, its delta or change vector, and any associated TSLU's. The modeloutputs a corrected NOx concentration (in the applicable units of lbsper mmBTU) for 40 CFR Part 60, Appendix GG compliance. The model outputsare recorded in the compliance database following averaging andscreening to 15 minute average blocks as required.

Element 304 of the PEM system may provide reporting capability forcompliance with 40CFR Part 75 and 40CFR Part 60 regulations and EDRgeneration capacities. This element may support system operators,interface with data acquisition devices, and can be run from anyworkstation on system 20.

The model may include additional components for enhancing utility. Inthe embodiment shown in FIG. 2, a PEMS Alarm Generator element 303 and aPEMS License Utility element 305 are incorporated into the PEMScomputing system. These additional components can optionally be providedby third parties and include a data display and alarm functionalityalong with report generation capabilities. These supplementary elementsmay optionally be installed on a separate computing device, eitherlocated onsite or remotely. These supplementary elements interact withthe predictive model or database for manipulation of the compliance datainto reports, graphs, real-time or historical displays.

In a particular embodiment, information generated by the predictiveelement of the system is used to predict an emissions profile of thesystem for comparison with applicable emissions standards, to evaluatecompliance with those standards. The predictive information generatedmay also be used by process control systems to adjust process variablesso as to prevent the occurrence of an out-of-compliance condition.

In another embodiment, the emissions monitoring and control systemdescribed herein includes means for providing feedback to elements ofthe control system (based on predetermined criteria for operation of theemissions source) for modifying system operating variables, tocompensate for deviations from normal operating parameters. Controlsignals responsive to the predicted emissions variable values may betransmitted to the process control system(s) of the emissions source(s).

It is expressly contemplated that any number of variables including, butnot limited to, carbon monoxide levels, nitrogen oxide levels, sulfurousoxide levels and oxygen could be predicted and controlled to facilitateany or all of the following: emission compliance, combustionoptimization, power output maximization, emission control through powersource optimization, emission control by addition of suitable agentssuch as nitrogen oxides, adsorbents of sulfurous oxides, steam or water.Any suitable variables for each emissions source can also be adjustedfor any of the above purposes. For example, the fuel feed rate, timing,air/fuel ratio, temperature, and amount of steam injection could bevaried to adjust the value of a desired emissions variable.

Any element of the PEMS system of the present invention may be stored onany suitable computer-readable storage medium (for example, CD-ROM,magnetic tape, internal or external hard drive, floppy disk(s), etc.) Inaddition, one or more components of the software may be transmitted ordownloaded via a signal communicated over a hard-wired connection orusing a wireless connection.

FIGS. 6, 7, and 8 show the results of a Subpart E analysis using apredictive model generated in accordance with the present invention asapplied to a gas turbine. The graphs used conform to formats found in 40CFR Part 75, Subpart E including the time plot of the PEMS vs. CEMS data(FIG. 6), the x-y plot of the PEMS vs. CEMS hour average data (FIG. 7),and the time plot of the differences between the PEMS and CEMS (FIG. 8).Procedures for certifying PEM systems are detailed in the regulations,namely 40 CFR Part 75, Subpart E and 40 CFR Part 60, Appendix B,Performance Specification 16, incorporated herein by reference. FIGS.6-8 show the extremely strong correlation between the predicted andactual values of NO, emissions achievable using the method describedherein.

In FIG. 9, a typical data flow example is provided. The nitrogen oxidesemissions from the gas-fired boiler are regulated in units of lbs of NOxper mmBTU of heat input. The formula for the calculation of NOx emissionrate in the applicable standard is obtained using EPA Method 19,Equation 19-1. The model is trained using raw dry NOx ppmv and Oxygen %concentration that is used to calculate the emission rate using Equation19-1. The constants used in formula are also provided in Method 19. Thepredicted NOx ppmv and Oxygen % are used to calculate the predicted NOxemission rate to be used for compliance determination.

The predictive model of the present invention can operate without a CEMSwhen certified as a primary continuous monitoring system for the sourcethrough a petition for approval of an alternate monitoring system (40CFR Part 75, Subpart E) or utilizing performance specification testingas promulgated by U.S. EPA (40 CFR Part 60, PS-16 draft).

The predictive model of the present invention can be retuned at any time(periodically or continuously) using existing CEMS equipment or bymobilizing temporary or mobile emission monitoring equipment andcollecting the process data concurrently.

The system and method of the present invention addresses thepreviously-described shortcomings of existing system. Using themethodology and software disclosed herein, a highly accurate predictiveemissions model may be generated for a given emissions source by atechnician having little or no understanding of the emissions source,the process run by the emissions source, or the theory or operation ofthe statistical hybrid model. The present invention allows owners andoperators of continuous or batch processes to build and maintainaccurate predictive model of the pollutant emission rates. Compared toexisting systems, the system described herein is less expensive andcomplicated to run and maintain. In addition, no special hardware isrequired. Thus, a predictive model embodying a method in accordance withthe present invention is unique in its ability to be developed bynon-specialized staff that has no familiarity with the process,pollution control, or the methodology used by the model. In addition,users of the model and third party consultants can update the modelwithout support of the manufacturer's engineering support. The processflow shown in FIGS. 4 and 5 is representative of a preferred mode ofimplementing the present invention. However, it should be understoodthat various modifications of the process flow could be used to providea different level of computational flexibility, depending on thecomplexity of the model, needed to address various data sources andregulatory schemes. The present invention contemplates any suitablevariation on this process flow.

Operation of the predictive model with respect to batch processes isalmost identical to its application to continuous processes. With regardto batch processes, the TSLU is critical to proper batch predictions,but is not based on time since last upset as previously defined. In thisinstance, the TSLU usually is defined as the time since the start of thebatch and can be compounded to include a leading integer to define thebatch type or loading. Batch processing is a series of disconnectedcontinuous operations each with a new TSLU incrementing from thebeginning of the batch to its conclusion by the base sampling interval.

The application of the present invention described herein relates topredicting emissions from processes for compliance purposes. Themethodology described herein may be used to develop a predictive schemefor any system comprising variables which are amenable to thecorrelative and statistical analyses described herein. Otherapplications of the invention not described herein, but considered fordevelopment include predicting weather patterns, predicting economic andfinancial patterns, predicting human behavior patterns among others arecontemplated but have not been explored to date.

It will be understood that the foregoing descriptions of embodiments ofthe present invention are for illustrative purposes only. As such, thevarious structural and operational features herein disclosed aresusceptible to a number of modifications commensurate with the abilitiesof one of ordinary skill in the art, none of which departs from thescope of the present invention as defined in the appended claims.

1. A method for generating a model representative of a process, theprocess including a result variable representing a product of theprocess, and a plurality of process variables representingcharacteristics of the process other than the product of the process,the method comprising the steps of: acquiring a plurality of test valuesof the result variable, each test value of the plurality of resultvariable test values being measured at a corresponding point in time;for each process variable of the plurality of process variables,acquiring a plurality of test values of the process variable, each testvalue of the plurality of process variable test values being associatedwith a result variable value of the plurality of result variable values,each test value of the plurality of process variable test values beingmeasured at a point in time substantially simultaneous with a point intime at which one of the test values of the plurality of result variabletest values is measured; for each first coefficient of a plurality offirst coefficients, providing a separate test value of the firstcoefficient associated with each process variable of the plurality ofprocess variables, each separate test value of the first coefficientbeing a function of at least a portion of the test values of theplurality of test values of the associated process variable; and foreach second coefficient of a plurality of second coefficients, providinga separate test value of the second coefficient associated with eachtest value of each process variable of the plurality of processvariables, each separate test value of the second coefficient being afunction of at least a portion of the test values of the plurality oftest values of the associated process variable.
 2. A computer systemincluding computer readable program code means stored in an elementthereof, for performing a method in accordance with claim
 1. 3. Acomputing device including computer readable program code means storedin a memory thereof for performing a method in accordance with claim 1.4. A non-transitory computer readable medium encoded with computerreadable instructions for performing a method in accordance withclaim
 1. 5. A predictive emissions monitoring system comprising anon-transitory computer readable medium in accordance with claim
 4. 6. Apower generation system comprising: an emissions source; and apredictive emissions monitoring system in accordance with claim 5operatively coupled to the emissions source.
 7. An article ofmanufacture comprising a non-transitory computer-usable medium havingcomputer-readable program code means embodied therein for performing amethod in accordance with claim
 1. 8. A computer data signal embodied ina non-transitory medium, the data signal comprising computer-readablesource code for performing a method in accordance with claim
 1. 9. Themethod of claim 1 further comprising the step of for each processvariable of the plurality of process variables, and using the pluralityof test values of the process variable, calculating an associated testcorrelation coefficient indicating a correlation between the processvariable and the characteristic.
 10. The method of claim 1 furthercomprising the step of for each process variable of the plurality ofprocess variables, and using the plurality of test values of the processvariable, calculating an associated test tolerance value specifying arange of values within which the test value of the process variable islocated.
 11. The method of claim 1 further comprising the step of foreach test value of the plurality of test values of each process variableof the plurality of process variables, calculating an associated testdelta value equal to a difference between the test value and amost-recent prior time-successive test value of the plurality of testvalues of the process variable.
 12. A method for predicting aquantitative measure of a characteristic of an emission from anemissions source, comprising the steps of: acquiring a plurality of testvalues of the characteristic, each test value of the plurality ofcharacteristic test values being measured at a corresponding point intime; for each process variable of a plurality of process variables,acquiring a plurality of test values of the process variable, each testvalue of the plurality of process variable test values being associatedwith a test value of the plurality of first variable test values, eachtest value of the plurality of process variable test values beingmeasured at a point in time substantially simultaneous with a point intime at which one of the test values of the plurality of first variabletest values is measured; for each process variable of the plurality ofprocess variables, and using the plurality of test values of the processvariable, calculating an associated test correlation coefficientindicating a correlation between the process variable and thecharacteristic; for each process variable of the plurality of processvariables, and using the plurality of test values of the processvariable, calculating an associated test tolerance value specifying arange of values within which the test value of the process variable islocated; for each test value of the plurality of test values of eachprocess variable of the plurality of process variables, calculating anassociated test delta value equal to a difference between the test valueand a most-recent prior time-successive test value of the plurality oftest values of the process variable; for each test value of theplurality of test values of each process variable of the plurality ofprocess variables, calculating an associated test indicator variablevalue indicating a result of a comparison between the tolerance valueassociated with the process variable value and the delta valueassociated with the process variable value; for each process variable ofselected ones of the plurality of process variables, acquiring aplurality of comparison values of the process variable; for each processvariable of the selected ones of the plurality of process variables andusing the plurality of comparison values of the process variable,calculating an associated comparison correlation coefficient indicatinga correlation between the process variable and the characteristic, foreach process variable of the selected ones of the plurality of processvariables and using the plurality of comparison values of the processvariable, calculating an associated comparison tolerance valuedescribing a range of values within which the comparison value of theprocess variable is located; for each comparison value of the pluralityof comparison values of each selected one of the plurality of processvariables, calculating an associated comparison delta value equal to adifference between the comparison value and a most-recent priortime-successive comparison value of the plurality of comparison valuesof the process variable; for each comparison value of the plurality ofcomparison values of each selected one of the plurality of processvariables, calculating an associated comparison indicator valueindicating a result of a comparison between the tolerance valueassociated with the process variable value and the delta valueassociated with the process variable value; for each process variable ineach predetermined combination of a plurality of predeterminedcombinations of the selected ones of the process variables, iterativelycomparing each comparison value of the variable with each test value ofthe variable, the comparison value of the tolerance associated with theprocess variable with the test value of the tolerance associated withthe process variable, the comparison value of the indicator associatedwith the process variable with the test value of the indicatorassociated with the process variable, the comparison value of the deltaassociated with the process variable with the test value of the deltaassociated with the process variable, and the comparison value of thecorrelation coefficient associated with the process variable with thetest value of the correlation coefficient associated with the processvariable; for each process variable in each predetermined combination ofa plurality of predetermined combinations of the selected ones of theprocess variables, identifying all test values of the additionalvariable where the test value of the additional variable differs from acomparison value of the additional variable by an amount equal to orless than a first predetermined amount, where the test value of thedelta associated with the test value of the additional variable differsfrom the comparison value of the delta associated with the comparisonvalue of the additional variable by an amount equal to or less than asecond predetermined amount, and where the test value of the indicatorassociated with the test value of the additional variable differs fromthe comparison value of the indicator associated with the comparisonvalue of the additional variable by an amount equal to or less than athird predetermined amount; and assigning, as the predicted value of theemissions variable, an average of all of the test values of theemissions variable that are associated with respective test values ofeach process variable for which the test process variable values differfrom the comparison process variable values by the associatedpredetermined amount.
 13. A computer system including computer readableprogram code means stored in an element thereof, for performing a methodin accordance with claim
 12. 14. A non-transitory computer readablemedium encoded with computer readable instructions for performing amethod in accordance with claim
 12. 15. A predictive emissionsmonitoring system comprising a non-transitory computer readable mediumin accordance with claim
 14. 16. A computer data signal embodied in anon-transitory computer readable medium, the data signal comprisingcomputer-readable source code for performing a method in accordance withclaim
 12. 17. A non-transitory computer readable medium encoded withcomputer readable instructions for performing a method for predicting avalue of a first variable based on values of a plurality of additionalvariables, the method comprising the steps of: acquiring a plurality oftest values of the first variable, each test value of the plurality offirst variable test values being measured at a corresponding point intime; for each additional variable of the plurality of additionalvariables, acquiring a plurality of test values of the additionalvariable, each value of the plurality of additional variable valuesbeing associated with a value of the plurality of first variable values,each test value of the plurality of additional variable test valuesbeing measured at a point in time substantially simultaneous with apoint in time at which one of the test values of the plurality of firstvariable test values is measured; for each first coefficient of aplurality of first coefficients, providing a separate test value of thefirst coefficient associated with each additional variable of theplurality of variables, each separate test value of the firstcoefficient being a function of at least a portion of the test values ofthe plurality of test values of the associated additional variable; foreach second coefficient of a plurality of second coefficients, providinga separate test value of the second coefficient associated with eachtest value of each additional variable of the plurality of variables,each separate test value of the second coefficient being a function ofat least a portion of the test values of the plurality of test values ofthe associated additional variable; for each selected one of a pluralityof selected ones of the additional variables of the plurality ofadditional variables, acquiring a plurality of comparison values of theadditional variable; for each first coefficient of the plurality offirst coefficients, providing a separate comparison value of the firstcoefficient associated with the additional variable, each separatecomparison value of the first coefficient being a function of at least aportion of the comparison values of the plurality of comparison valuesof the associated additional variable; for each second coefficient ofthe plurality of second coefficients, providing a separate comparisonvalue of the second coefficient associated with the comparison value ofeach additional variable, each separate comparison value of the secondcoefficient being a function of at least a portion of the comparisonvalues of the plurality of comparison values of the associatedadditional variable; for each additional variable in each predeterminedcombination of a plurality of predetermined combinations of the selectedones of the additional variables, iteratively comparing: each comparisonvalue of the additional variable with each test value of the additionalvariable; and the comparison values of selected ones of the secondcoefficients associated with the comparison value of the variable withthe test values of the selected ones of the second coefficientsassociated with the test value of the variable; for each additionalvariable in each predetermined combination of a plurality ofpredetermined combinations of the selected ones of the additionalvariables, identifying all test values of the additional variable wherethe test value differs from a comparison value of the additionalvariable by an amount equal to or less than an associated predeterminedamount, and where, for each of the selected ones of the secondcoefficients associated with each test value of the additional variable,all test values of the selected ones of the second coefficients differfrom the comparison values of the selected ones of the secondcoefficients by an amount equal to or less than an associatedpredetermined amount; and assigning, as the predicted value of the firstvariable, an average of all of the test values of the first variablethat are associated with respective test values of each additionalvariable for which the test first variable values differ from thecomparison additional variable values by the associated predeterminedamount.
 18. The non-transitory computer readable medium of claim 17wherein the computer readable medium comprises a memory in a computingdevice.
 19. The non-transitory computer readable medium of claim 17wherein the computer readable medium comprises a memory in a computersystem.
 20. The non-transitory computer readable medium of claim 17wherein the computer readable medium comprises a compact disc.
 21. Apredictive emissions monitoring system comprising a non-transitorycomputer readable medium in accordance with claim
 17. 22. A powergeneration system comprising: an emissions source; and a predictiveemissions monitoring system in accordance with claim 21 operativelycoupled to the emissions source.
 23. An article of manufacturecomprising a non-transitory computer-readable medium in accordance withclaim 17.